A data model is a repository of all of the information we may want to hold for our application. The DOM is the representation of the data model that is accessbile to users via their browswer.
As one person put it, the library is the mother, the framework is the father; frameworks generally have more rules and restrictions of where to use their code. Additionally, frameworks will eventually need to reference or 'ask' its library at some point in order for it to do anything with it. A library on the other hand is readily accessible no matter most situations and we can directly reference its functionality.
The main purpose of a framework is so that it keeps the UI in sync with the state/data being manipulated. Doing so in Vanilla JS can be complicated on anything even slighly complex and even doing it successfully, resembles something of a framwork anyway.
A component is code that is used in react that is reusable and can be used to render html code to the DOM via JSX or manipulate data in some way that can be represented on the DOM. If you code it dynamically, it allows you code that is reusable. Additionally, because one component can be used with smaller components within it, at the top level, reading through code becomes easier as that top level component (sometimes called an App) may act as a table of contents for the reader
JSX is what React uses to allow us to write HTML in javascript. Without React, anything that looks like html will not be interpreted as such. It is HTML code in Javascript clothing.
Props are properties that get passed from one component to another as arguments and are generally passed down from parent to child components
State is where the data we want to affect is being stored. Ideally, anytime the 'state' or the data model changes, we want to re-render that information as it is represented on the virtual dom
Data down, action up has to do with how data is passed down from a parent component to a child component and then having the child use that data in some way that notifies the parent element.